Math Problem Statement

Compute the total and annual returns on the described investment. Six years after buying 150 shares of XYZ stock for ​$60 per​ share, you sell the stock for $14,400. Question content area bottom Part 1 The total return is enter your response here​%. ​(Do not round until the final answer. Then round to one decimal place as​ needed.) Part 2 The annual return is . ​(Do not round until the final answer. Then round to one decimal place as​ needed.)

Solution

Let's break the problem into two parts: calculating the total return and then the annual return.

Part 1: Total Return

The total return is given by the formula:

Total Return(%)=(Final ValueInitial ValueInitial Value)×100\text{Total Return} (\%) = \left( \frac{\text{Final Value} - \text{Initial Value}}{\text{Initial Value}} \right) \times 100

Step 1: Initial Value

You bought 150 shares at $60 per share:

Initial Value=150×60=9000USD\text{Initial Value} = 150 \times 60 = 9000 \, \text{USD}

Step 2: Final Value

You sold the shares for $14,400, so the Final Value is $14,400.

Step 3: Calculate Total Return

Now, substitute the values into the total return formula:

Total Return=(1440090009000)×100\text{Total Return} = \left( \frac{14400 - 9000}{9000} \right) \times 100

I'll calculate that next.

Part 2: Annual Return

The annual return can be calculated using the formula for the compound annual growth rate (CAGR):

Annual Return(%)=((Final ValueInitial Value)1n1)×100\text{Annual Return} (\%) = \left( \left( \frac{\text{Final Value}}{\text{Initial Value}} \right)^{\frac{1}{n}} - 1 \right) \times 100

where:

  • Final Value=14400\text{Final Value} = 14400
  • Initial Value=9000\text{Initial Value} = 9000
  • n=6n = 6 (the number of years)

Now let's calculate both the total return and the annual return.### Part 1: Total Return The total return is 60.0%.

Part 2: Annual Return

The annual return is approximately 8.1%.

Would you like any more details or further clarification?

Here are 5 related questions to consider:

  1. What factors could affect the annual return on investments?
  2. How does compounding impact the annual return over different periods?
  3. What is the difference between simple interest and compound interest in long-term investments?
  4. How does stock price volatility affect potential total returns?
  5. How can you assess the risk of an investment based on its historical returns?

Tip: Always factor in inflation when assessing the real value of your investment returns over time.

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Math Problem Analysis

Mathematical Concepts

Percentage
Compound Interest
Investment Returns

Formulas

Total Return (%) = ((Final Value - Initial Value) / Initial Value) × 100
Annual Return (%) = ((Final Value / Initial Value)^(1/n) - 1) × 100

Theorems

Compound Annual Growth Rate (CAGR)

Suitable Grade Level

Grades 10-12